At a gas station, 35% of the customers buy economy gas, 25% of the customers buy regular gas, 30% buy mid-grade gas, and 10% buy premium gas. Of those customers buying economy gas, only 40% fill their tanks. Of those buy regular gas, only 30% fill their tanks. Of those customers buying mid-grade gas, 60% fill their tanks, whereas of those buying premium, 50% fill their tanks. a) What is the probability that the next customer will request premium gas and fill the tank? b) What is the probability that the next customer fills the tank? c) If the next customer fills the tank, what is the probability that regular gas is requested? d) If the next customer does not fill the tank, what is the probability that premium gas is requested?